Multiple Choice Choose the statement that is not true. Assume b ≠0, c ≠0, and d ≠0 as necessary.

step 1 So we're given these multiple choices, A, B, C, and D, and I highlighted those in yellow, so we

Multiple Choice Choose the statement that is not true....

Multiple Choice Choose the statement that is not true. Assume $b \neq 0, c \neq 0,$ and $d \neq 0$ as necessary. (a) $\frac{a c}{b c}=\frac{a}{b}$ (b) $\frac{a}{b}+\frac{c}{b}=\frac{a+c}{b}$ (c) $\frac{a}{b}-\frac{c}{d}=\frac{a d-b c}{b d}$ (d) $\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a c}{b d}$

Multiple Choice Choose the statement that is not true. Assume
$b \neq 0, c \neq 0,$ and $d \neq 0$ as necessary.
(a) $\frac{a c}{b c}=\frac{a}{b}$
(b) $\frac{a}{b}+\frac{c}{b}=\frac{a+c}{b}$
(c) $\frac{a}{b}-\frac{c}{d}=\frac{a d-b c}{b d}$
(d) $\frac{\frac{a}{b}}{\frac{c}{d}}=\frac{a c}{b d}$

Key Concepts

Multiplication of Fractions

Multiplying two fractions involves multiplying their numerators together and their denominators together. The concept of cancelling common factors before or after the multiplication is an important technique to simplify the product to its simplest form.

Division of Fractions

Dividing one fraction by another incorporates the concept of multiplying by the reciprocal of the divisor. This key concept underlines that the division of two fractions is not computed by simply dividing their numerators and denominators directly but by flipping the second fraction and then performing a multiplication, ensuring that all algebraic manipulations conform to the standard rules.

Properties of Fractions

This concept covers the fundamental rules for operations with fractions, such as the cancellation of common factors in numerators and denominators, addition and subtraction of fractions with common denominators, as well as multiplication and division. Understanding how these operations work is crucial to correctly manipulate fractions and to see when certain algebraic simplifications are valid.

Addition and Subtraction of Fractions

This key concept explains that fractions with a common denominator can be directly added or subtracted by performing the arithmetic operations on the numerators while retaining the denominator. It also addresses the method required when fractions have different denominators, involving finding a common denominator, which is a critical step to combine them into a single fraction.

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